The earliest iris that blooms in the spring is the miniature iris reticulata that has little purple flowers with a yellow dot on the falls. Generally, all the shorter iris types bloom earliest, starting the parade of iris flowers that continues throughout the summer.
The large bearded German iris bloom with the peonies in May, and the tall graceful Siberian iris are quite early, too, with beardless flowers that seem to dance like ballerinas.
June brings that large flat Japanese iris into bloom with their large mauve, pink, purple, and white flowers.
The English iris bloom early to mid summer. These originated in Spain and were taken to England by merchant seamen.
Dutch iris are rather new on the horticultural scene and grow from bulbs. They were hybridized fairly recently by Dutch growers who crossed Spanish iris with other species. They love soil that is warm and dry during the summer months. They are hardy to zone 6, or 5 if mulched.
One of my favorites is the Louisiana iris that likes moist soil so thrives around my water fountain. Black gamecock is an exquisite dark purple.
Spurias bloom late, too, and are the tallest iris and never need to be divided. And the robust Juno iris introduced from Turkey in 1889 is the last iris to bloom in my zone 5 garden.